Perforation strategy

ABSTRACT

A method includes determining a stress variation of a geological formation disposed on a wellbore; determining a breakdown pressure of each perforation of a plurality of perforations along a length of the wellbore based on the stress variation; calculating a flow rate of a pumping operation of a hydraulic fracturing process based on the breakdown pressure of each perforation of the plurality of perforations; and hydraulically fracturing a geological formation disposed on the wellbore based on the flow rate.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to U.S. Provisional Patent Application Ser. No. 61/919,636 filed on Dec. 20, 2013 and entitled, “Method to Prevent Fracture Overflushing Using Sacrificial Fracture”; U.S. Provisional Patent Application Ser. No. 62/000,914 filed on May 20, 2014 and entitled, “Method for Determining Perforation Flow Rates in Cased Hole Hydraulic Fracturing Applications”; U.S. Provisional Patent Application Ser. No. 62/001,321 filed on May 21, 2014 and entitled, “Modified Shale Step Down Test”; and U.S. Provisional Patent Application Ser. No. 62/058,421 filed on Oct. 1, 2014 and entitled, “Perforation Strategy” under 35 U.S.C. §119(e). U.S. Provisional Patent Application Ser. Nos. 61/919,636; 62/000,914; 62/001,321; and 62/058,421 are hereby incorporated in their entirety.

BACKGROUND

In general, operations, such as geophysical surveying, drilling, logging, well completion, hydraulic fracturing, steam injection, and production, are typically performed to locate and gather valuable subterranean assets, such as valuable fluids or minerals. The subterranean assets are not limited to hydrocarbons such as oil or gas. After gathering valuable subterranean assets, operations such as well abandonment may involve the sealing of a well to safely and economically decommission a well.

SUMMARY

In one aspect, a method according to one or more embodiments may include determining a stress variation of a geological formation disposed on a wellbore; determining a breakdown pressure of each perforation of a plurality of perforations along a length of the wellbore based on the stress variation; calculating a flow rate of a pumping operation of a hydraulic fracturing process based on the breakdown pressure of each perforation of the plurality of perforations; and hydraulically fracturing a geological formation disposed on the wellbore based on the flow rate.

In one aspect, a method according to one or more embodiments may include determining a stress variation of a geological formation disposed on a wellbore; generating a first plurality of perforations having a having a first breakdown pressure and a second plurality of perforations having a second breakdown pressure greater than the first breakdown pressure based on the stress variation; hydraulically fracturing a first portion of the geological formation corresponding to the first plurality of perforations; isolating the first plurality of perforations; hydraulically fracturing a second portion of the geological formation corresponding to the second plurality of perforations.

In one aspect, a method according to one or more embodiments may include determining a stress variation of a geological formation disposed on a wellbore; generating a first plurality of perforation groups having a first breakdown pressure based on the stress variation; generating a second plurality of perforation groups having a second breakdown pressure based on the stress variation; hydraulically fracturing a first portion of the geological formation corresponding to the first plurality of perforation groups; isolating the first plurality of perforation groups; and hydraulically fracturing a second portion of the geological formation corresponding to the second plurality of perforation groups.

In one aspect, a method according to one or more embodiments may include pumping a fluid into a wellbore at a first rate for a first period of time and determining a first bottom hole pressure; determining a rate of change of the first bottom hole pressure during the first time period; and normalizing the determined rate of change of the bottom hole pressure to a volume of the fluid pumped during the first time period.

BRIEF DESCRIPTION OF DRAWINGS

Certain embodiments of the disclosure will be described with reference to the accompanying drawings. However, the accompanying drawings illustrate certain aspects or implementations by way of example and are not meant to limit the scope of the claims.

FIG. 1 shows a method of producing hydrocarbons in accordance with one or more embodiments of the disclosure.

FIG. 2 shows an example plot of stress along a wellbore in accordance with one or more embodiments of the disclosure.

FIG. 3 shows an example plot of an analytical calculation of stresses about a cross section of a wellbore in accordance with one or more embodiments of the disclosure.

FIG. 4 shows three perforations about a wellbore superimposed on a plot of the stresses about the wellbore in accordance with one or more embodiments of the disclosure.

FIG. 5 shows an example plot of stress along a wellbore and two potential perforation groups in accordance with one or more embodiments of the disclosure.

FIG. 6 shows a sacrificial fracture and production fractures along a wellbore in accordance with one or more embodiments of the disclosure.

FIG. 7 shows fractures corresponding to production fractures along a wellbore in accordance with one or more embodiments of the disclosure.

FIG. 8 shows two sets of perforations along a wellbore in accordance with one or more embodiments of the disclosure.

FIG. 9 shows fractures corresponding to two sets of perforations along a wellbore in accordance with one or more embodiments of the disclosure.

FIG. 10 shows two sets of perforations along a wellbore in accordance with one or more embodiments of the disclosure.

FIG. 11 shows fractures corresponding to two sets of perforations along a wellbore in accordance with one or more embodiments of the disclosure.

FIG. 12 shows a plot of a modified step-down measurement in accordance with one or more embodiments of the disclosure.

FIGS. 13A-13C show example plots of outcomes of the modified step-down measurement in accordance with one or more embodiments of the disclosure.

FIG. 14 shows a computer system in accordance with one or more embodiments of the disclosure.

DETAILED DESCRIPTION

Specific embodiments will now be described with reference to the accompanying figures. In the following description, numerous details are set forth as examples of the disclosure. It will be understood by those skilled in the art that one or more embodiments of the disclosure may be practiced without these specific details and that numerous variations or modifications may be possible without departing from the scope of the disclosure. Certain details known to those of ordinary skill in the art are omitted to avoid obscuring the description.

Embodiments disclosed herein are directed toward hydraulic fracturing processes. A hydraulic fracturing process is a method of fracturing a target by the application of pressurized fluids. By applying pressurized fluids to a target, pressure may be applied to the target by the fluids. Increasing the pressure of the fluids applied to the target may increase the pressure applied to the target. If an applied pressure reaches a breakdown pressure of a target, the target may fracture in response to the applied pressure.

In one or more embodiments of the disclosure, the target may be a geological formation. For example, an oil field well may be located on a geological formation and may include a wellbore that extends into the geological formation. The geological formation may include various types of rock, dirt, sediment, and other subterranean formations.

Within a geological formation, hydrocarbon bearing fluids may exist. However, due to the structure of the geological formation, the hydrocarbon bearing fluids may not be mobile within the geological formation. When an oil field well is drilled into the geological formation, it may not be possible to extract hydrocarbon bearing fluids from the geological formation due to the immobility of the hydrocarbon bearing fluids.

In one or more embodiments of the disclosure, a hydraulic fracturing process may be applied to the geological formation. The hydraulic fracturing process may include determining the stresses surrounding the wellbore, perforating the wellbore based on the determined stresses, determining the flow rate of each perforation, hydraulically fracturing the geological formation based on the flow rates, and characterizing the flow rate of the hydraulic fracture. The well may produce hydrocarbon bearing fluids based on the determined flow rate the hydraulic fracture.

Embodiments of the disclosure are not limited to oil field applications and may be employed in a diverse array of applications. For example, embodiments of the disclosure may be employed to hydraulically fracture stone structures such as granite slabs or manmade concrete structures.

FIG. 1 shows a flowchart (100) according to one or more embodiments of the disclosure. The method depicted in FIG. 1 may be used to produce hydrocarbon bearing fluids from a well in accordance with one or more embodiments of the disclosure. One or more items shown in FIG. 1 may be omitted, repeated, and/or performed in a different order among different embodiments.

At item 10000, the stresses surrounding a wellbore are determined. The stresses surrounding a wellbore may vary along the length of the wellbore due to the geological formation and about the wellbore due to the stresses induced by drilling and completing the wellbore. In one or more embodiments of the disclosure, the stresses surrounding the wellbore may be determined by direct measurement, computational modeling, or analytical calculations.

Direct measurement of the stresses surrounding the wellbore may include acoustic measurements as known in the art. An acoustic tool may be placed into the wellbore. The acoustic tool may then be moved along the wellbore. As the acoustic tool moves, acoustic energy may be radiated into the wellbore and geological formation surrounding the wellbore. A portion of the acoustic energy may be received by the acoustic tool and the stresses surrounding the wellbore may be determined by the received acoustic energy, as known in the art.

An example plot (200) of the measured stress along the length of the wellbore is shown in FIG. 2. The horizontal axis of the plot may correspond to a position along the wellbore and the vertical axis may correspond to a measured stress. Portions of the plot are shaded based to indicates sections of the wellbore having approximately the same level of stress. As seen from FIG. 2, the stresses along a wellbore may vary with position along the wellbore. Portions of the wellbore may have similar level of stress while other portions of the wellbore may have different levels of stress.

Computational models or analytical calculations may be used to determine the local stresses surrounding a wellbore at a specific location along the wellbore, as known in the art. An analytical solution to the stress surrounding a cross section of a wellbore may be used to estimate the stresses surrounding the wellbore.

FIG. 3 shows an example plot (300) plot of an analytical calculation for the stresses surrounding a wellbore, as known in the art. Specifically, the example plot (300) shows the Amadei solution to the stresses surrounding a circular wellbore (310). The horizontal axis corresponds to a distance along a first axis of the cross section of the wellbore (310) and the second axis corresponds to a distance along the second axis of the cross section of the wellbore (310). The example plot (300) shading indicates the pressure intensity, normalized to a nominal level. As seen from the example plot (300), the stresses around the wellbore (310) vary. The stresses may include a lower stress region (320) and a higher stress region (330).

The analytical solution shown in FIG. 3 ignores imperfections in the wellbore (310) that may be caused by inadvertent completion errors. For example, the wellbore (310) may include a casing of concrete that is thicker in some sections and thinner in others. To improve the accuracy of the determined stresses, a computational solution, as known in the art, may be used to accurately calculate the local stresses around the wellbore. The computational solution may calculate the variation of the wellbore by incorporating direct measurements of the structure of the wellbore. For example, acoustic measurements, as previously discussed, may be used to determine the variation of the wellbore, such as a casing thickness, directly. Directly determining the variation of the wellbore based on measurements of the wellbore may improve the accuracy of the stresses determined by the computational solution.

Returning to FIG. 1, at item 10100, the wellbore is perforated based on the determined stresses. A wellbore perforation is a passageway leading from the interior of the wellbore outward into the geological formation. A perforation may be formed by a perforation gun, as known in the art.

A perforation may be used to allow pressurized fluids pumped into the wellbore to interact with the geological formation surrounding the wellbore. The passageway formed by each perforation may allow pressurized fluids to flow out of the wellbore and apply pressure to the surrounding geological formation. If the pressure applied by the pressurized fluids is greater than the geological formation stress at the location of the applied pressure, a portion of the geological formation near the location of the applied pressure may fracture. Fracturing a portion of the geological formation may generate channels throughout the portion of the geological formation. By generating channels, fluids may traverse the portion of the geological formation based on fluid pressures.

For example, when a portion of a geological formation fractures, fluids may flow into the geological formation from the wellbore. Similarly, hydrocarbon bearing fluids contained in the geological formation surrounding the wellbore may flow into the wellbore by the generated fractures. The direction of fluid flow may depend on the stresses within the geological formation and the fluid pressure within the wellbore. When the stresses within the geological formation are greater than the fluid pressure within the wellbore, fluids within the geological formation may flow into the wellbore. Conversely, when the stresses with the geological formation are less than the fluid pressure within the wellbore, fluids with the wellbore may flow into the geological formation.

In one or more embodiments of the disclosure, each perforation of a hydraulic fracturing procedure is formed based on the observed stresses. As shown in FIGS. 2 and 3, the stresses along the wellbore and the local stresses surrounding any cross section of a wellbore may vary. When a perforation is formed, the perforation will have an associated breakdown pressure. The breakdown pressure of the perforation is the pressure that, if applied to the perforation, may fracture a portion of the geological formation corresponding to the perforation.

By estimating or calculating the stresses surrounding the wellbore, as determined in item 10000 (FIG. 1), perforations may be tailored to obtain a desired breakdown pressure for a subsequent hydraulic fracturing of a hydraulic fracturing process. Generating a perforation by a perforation gun, as known in the art, is a well understood and controlled process. For example, a perforation may be generated by a perforation gun having a predetermined depth of penetration, phasing, and diameter by selecting appropriate quantities and types of explosives and projectiles, respectively. Phasing is the direction of the perforation with respect to the wellbore. For example, a 60° phasing indicates a perforation direction corresponding to a location 60° down from a reference point on the wellbore, e.g. 60° from the top of the wellbore or 60° up from the bottom of the wellbore. Accordingly, by knowing stresses surrounding the wellbore, perforations having a predetermined breakdown pressure may be generated.

FIG. 4 shows an example of three perforations superimposed on the example plot (300) of the analytical calculation for the stresses surrounding a wellbore in accordance with one or more embodiments of the disclosure. The plot (300) includes a first perforation (400), a second perforation (410), and a third perforation (420). Each perforation is directed outward into the geological formation surrounding the wellbore. The perforation depth and location of each perforation is different, as seen from FIG. 4.

Due to the difference in perforation depth and location, with respect to the wellbore, the breakdown pressure of each perforation is different. As seen from FIG. 4, the stresses surrounding the wellbore vary based on location and therein changes in the location or depth of a perforation cause the perforation to interact with different levels of stress. For example, the first perforation (400) may have a low breakdown pressure. As seen from FIG. 4, the first perforation (400) extends into a region of the geological formation where the stresses are approximately 7500 psi. Accordingly, if pressurized fluids are pumped into the wellbore and exert greater than 7500 psi, the region of the geological formation near the first perforation (400) may fracture.

In another example, the second perforation (410) may have a moderate breakdown pressure. As seen from FIG. 4, the second perforation (410) extends into a region of the geological formation where the stresses are approximately 9000 psi. Accordingly, if pressurized fluids are pumped into the wellbore and exert greater than 9000 psi, the region of the geological formation near the second perforation (410) may fracture.

In an additional example, the third perforation (420) may have a high breakdown pressure. As seen from FIG. 4, the third perforation (410) extends into a region of the geological formation where the stresses are approximately 13000 psi or greater. Accordingly, if pressurized fluids are pumped into the wellbore and exert greater than 13000 psi, the region of the geological formation near the second perforation (410) may fracture.

As seen from the above examples, by determining the local stresses around the wellbore, perforations having an engineered or tailored breakdown pressure may be generated. Similarly, by determining the stresses along the length of the wellbore, perforations having engineered breakdown pressures may be generated.

FIG. 5 shows the example plot (200) of the measured stress along the length of the wellbore as shown in FIG. 2 and two potential sets of perforations. Specifically, FIG. 5 shows a first potential set of perforations (500) in a wellbore (510) and a second potential set of perforations (520) in the wellbore (510).

The first potential set of perforations (500) includes 5 groups of perforations, commonly referred to as a cluster, located at discrete locations along the wellbore. As seen from the example plot (200) of the stresses (210) along the wellbore, the stresses vary along the length of the wellbore. Due to the variation in the stresses (210) along the wellbore, each group of perforations of the first potential set of perforations (500) may have a different average breakdown pressure. Graphical representations (505) of the average breakdown pressure associated with each group of perforations are shown above each group of perforations. The height and shading of each of the graphical representations (505) corresponds to an average breakdown pressure associated with each group of perforations. Additionally, the shading of each graphical representation (505) corresponds to a shading on the example plot (200) and therein indicates the measured stresses at each location of each group of perforations.

As seen from the graphical representations (505), the average breakdown pressure associated with each group of perforations of the first potential set of perforations (500) varies. In some cases, it may not be desirable for each group of perforations to have a different breakdown pressure. For example, to fracture the first potential set of perforations (500) the pressure within the wellbore is raised to a level greater than the highest breakdown pressure associated with any group of perforations clusters. Due to the variation in stress along the wellbore and the location of each group of perforations of the first potential set of perforations (500), the pressure within the wellbore is raised to a high level as indicated by the graphical representations (505). Additionally, as the pressure in the wellbore is raised by pumping fluids into the wellbore some perforations groups may breakdown at pressures lower than the high level needed to breakdown the groups of perforations. If a group of perforations breakdown before the wellbore reaches the high level of pressure needed to breakdown the groups of perforations, pressurized fluids may flow into the geological formation and therein make generating the high level of pressure in the wellbore more difficult, time consuming, and costly.

By determining the stresses along the wellbore in item 10000 (FIG. 1), the location of each group of perforations along a wellbore may be selected to engineer or tailor a breakdown pressure of a perforation or group of perforations. The location of each group of perforations along a wellbore may be selected, based on the measured stress along the wellbore, to modify a subsequent fracturing process. For example, the location of each group of perforations along the wellbore may be selected to set the breakdown pressure of each group of perforations to a uniform level.

FIG. 5 shows a second potential set of perforations (500) that includes 4 groups of perforations located at locations along the wellbore having an approximately equal level of stress. As seen from the example plot (200) of the stresses (210) along the wellbore, sections of the wellbore may have approximately equal levels of stresses at different locations. By locating each group of perforations at locations of approximately equal stress, each group of perforations of the second potential set of perforations (500) may have an approximately equal breakdown pressure. Graphical representations (525) of the breakdown pressure associated with each group of perforations are shown above each group of perforations. The height and shading of each of the graphical representations (525) corresponds to a breakdown pressure associated with each group of perforations. Additionally, the shading of each graphical representation (525) corresponds to a shading on the example plot (200) and therein indicates the measured stresses at each location of each group of perforations.

However, in some cases, it may not be practical or possible to locate the perforations (500) at locations along the wellbore having approximately equal levels of stress. For such cases, the depth, phasing, or diameter of each parameter may be adjusted to equalize the average breakdown pressure associated with each group of perforations to a level. In one or more embodiments of the disclosure, the phasing of each perforation or group of perforations is selected, tailored, engineered, or otherwise determined to equalize the breakdown pressure of individual or groups of perforations.

As seen from the graphical representations (525), the average breakdown pressure associated with each group of perforations of the second potential set of perforations (520) may be approximately equal. In some hydraulic fracturing processes, it may be desirable for each group of perforations to have an approximately equal average breakdown pressure. For example, to fracture the second potential set of perforations (520) the pressure within the wellbore is raised to a level greater than the highest breakdown pressure associated with any group of perforations clusters. Due to the approximately equal level of the breakdown pressure associated with each perforation of the second potential set of perforations (520), the perforations may breakdown at a pressure that is approximately the same level and therein may improve a subsequent hydraulic fracturing process.

Thus, as seen in FIGS. 4 and 5, perforations having an engineered or tailored breakdown pressure may be formed by selecting a location of the perforation along the wellbore, a perforation depth, and a perforation direction around the wellbore. By measuring, simulating, or calculating the pressures along the wellbore, according to embodiments of the disclosure, the location, perforation depth, and perforation direction with respect to the wellbore for each perforation may be determined.

In one or more embodiments of the disclosure, the wellbore may be perforated based on the determined stresses and a to-be-performed hydraulic fracturing of the geological formation. In other words, the wellbore may be perforated as part of an overall hydraulic fracturing strategy that includes perforating the wellbore and the hydraulic fracturing. By perforating the wellbore based on an overall hydraulic fracturing strategy, the cost of hydraulically fracturing the well may be decreased and the production of hydrocarbon baring fluids from the well may be improved when compared with traditional hydraulic fracturing procedures.

In one or more embodiments of the disclosure, the to-be-performed hydraulic fracturing may include includes a diversion process. A diversion process, as known in the art, is a method of temporarily closing a perforation that has been previously fractured. By temporarily closing a perforation or group of perforations, the perforations may be isolated from subsequent processes of the hydraulic fracturing. For example, a wellbore may include a first set of perforations having a lower breakdown pressure and a second group of perforations having a higher breakdown pressure. The geological formation may be hydraulically fractured by first pumping pressurized fluids into the wellbore until the pressure in the wellbore exceeds the lower breakdown pressure. The first set of perforations may breakdown in response to the first pumping. The first perforations may then be temporarily sealed by a diversion process, as known in the art.

The diversion process may include pumping a fluid, containing a fiber or other material, into the wellbore. The fiber or other material may be directed into each of the first set of perforations by the flow of the fluid. Upon entering each perforation, the fiber or other material contained in the fluid may accumulate and seal each perforation. By sealing each perforation of the first set of perforations, the hydraulic fracture associated with each perforation of the first set of perforations may be sealed.

The diversion process may include pumping a fluid and a number of balls corresponding to the number of perforations of the first set of perforations. The balls may be directed into each perforation of the first set of perforations by the flow of the fluid. A ball may lodge at the entrance of each perforation of the first set of perforations along the wellbore and therein temporarily seal each broken down perforation of the first set of perforations.

The diversion process may include pumping a fluid and a number of balls greater than or less than the number of perforations of the first set of perforations. The balls may be directed into each perforation of the first set of perforations by the flow of the fluid. A ball may lodge at the entrance of each perforation of the first set of perforations along the wellbore and therein temporarily seal each broken down perforation of the first set of perforations. By including a number of balls greater than the number of perforations of the first set of perforations, sealing of the perforations may be improved because in some cases more than one ball may lodge at each perforations. By including a number of balls less than the number of perforations of the first set of perforations, the probability of breaking down a second set of perforations having a high breakdown pressure may be improved.

Once the first set of perforations are temporarily sealed, the pressure in the wellbore may be raised to the higher breakdown pressure. By temporarily sealing the first set of perforations, fluid flow out of the wellbore and into the geological formations may be reduced or eliminated as the pressure in the wellbore is raised to the higher breakdown pressure. The second set of perforations may breakdown in response to the pressure in the wellbore being raised to the higher breakdown pressure. Thus, hydraulic fracturing including at least one diversion process may selectively breakdown groups of perforations sequentially.

In one or more embodiments of the disclosure, a first perforation strategy may include generating a number of production perforations having a lower breakdown pressure and one or more sacrificial perforations having a higher breakdown pressure. The first perforation strategy may be used to divert an overflush of a hydraulic fracturing process, as known in the art, to the sacrificial perforations. By diverting the overflush to sacrificial perforations, the overflush may be prevented from entering the production perforations.

FIG. 6 shows a wellbore (600) having perforations corresponding to the first perforation strategy according to one or more embodiments of the disclosure. A plot of the measured stress (615) along the wellbore is also shown. As seen from the plot of the measured stress (615), the measured stress (615) varies along the length of the wellbore.

In one or more embodiments of the disclosure, the location of each of the number of production perforations (605) is selected to correspond to a low stress section of the wellbore and the location of the sacrificial perforations (610) corresponds to a high stress section of the wellbore. Thus, production perforations (605) having a location along the wellbore selected based on the measured stresses (615) may have an approximately equal breakdown pressure that is lower than the breakdown pressure of the one or more sacrificial perforations (610). However, the first perforation strategy is not limited to engineering or tailoring of the breakdown pressure of the production perforations (605) or the sacrificial perforations (610) by determining a location of each perforation. As discussed above, the perforation depth or perforation direction (phasing) may be determined to engineering or tailor the breakdown pressure of each perforation without departing from the scope of the disclosure.

Once the production perforations (605) and one or more sacrificial perforations (610) have been formed, the geological formation surrounding the wellbore (600) may be hydraulically fractured. Hydraulic fracturing may include pumping fluids into the wellbore until the production perforations (605) are broken down.

FIG. 7 shows the wellbore (600) after breaking down the production perforations (605) in accordance with one or more embodiments of the disclosure. Breaking down the production perforations (605) may generate fractures (700), extending into the geological formation surrounding the wellbore (600), corresponding to the production perforations (605). By generating the fractures (700), the mobility of fluids in the geological formation may be improved. Once the production perforations (605) are broken down, a proppant, as known in the art, may be pumped into the fractures (700) to prevent the fractures (700) from sealing. In some embodiments other fracturing processes may be employed without departing from the scope of the disclosure. For example, acid fracturing may be employed with corresponding pumping processes with diverting from the scope of the disclosure.

After pumping the proppant into the fractures (700), a diversion material, such as balls, degradable balls, or any other material or method as known in the art, may be pumped into the wellbore (600) to temporarily seal the production perforations. Once the production perforations (605) are sealed, the pressure in the wellbore may be increased to breakdown the one or more sacrificial perforations (610). By breaking down the one or more sacrificial perforations (610) while the production perforations (605) are sealed, the overflush may be diverted into the sacrificial fractures (610). Thus, the first perforation strategy may enable overflush fluids to be diverted into the sacrificial fractures (610) rather than the production fractures (605).

In one or more embodiments of the disclosure, a second perforation strategy may include generating groups of production perforations having an alternating breakdown pressure. The second perforation strategy may be used to more uniformly fracture the geological formation.

FIG. 8 shows a wellbore (800) including high breakdown pressure perforations (810) and low breakdown pressure perforations (820) in accordance with one or more embodiments of the disclosure. As seen from FIG. 8, the perforations are arranged as alternating groups of high breakdown pressure perforations (810) and low breakdown pressure perforations (820). In one or more embodiments of the disclosure, the perforation depth and perforation direction of each of the perforations is selected to engineer the breakdown pressure of each perforation to correspond to a high breakdown pressure or a low breakdown pressure.

Once the perforations are formed, the geological formation surrounding the wellbore (800) may be hydraulically fractured. Hydraulic fracturing may include pumping fluids into the wellbore until the low breakdown pressure perforations (820) are broken down.

FIG. 9 shows the wellbore (800) after breaking down the low breakdown pressure perforations (820) in accordance with one or more embodiments of the disclosure. Breaking down the low breakdown pressure perforations (620) may generate a first set of fractures (900), extending into the geological formation surrounding the wellbore (800), corresponding to the low breakdown pressure perforations (820). Once the low breakdown pressure perforations (820) are broken down, a proppant, as known in the art, may be pumped into the first set of fractures (900) to prevent the first set of fractures (900) from sealing.

After pumping the proppant into the first set of fractures (900), a diversion material, such as balls, degradable balls, or any other material or method as known in the art, may be pumped into the wellbore (800) to temporarily seal the low breakdown pressure perforations (820). Once the low breakdown pressure perforations (820) are sealed, the pressure in the wellbore may be increased to breakdown the high breakdown pressure perforations (810). By breaking down the high breakdown pressure perforations (810) the fluid mobility within the geological formation may be improved. Thus, the second perforation strategy may improve the flow of fluid within a geological formation surrounding a wellbore (800). Embodiments of the disclosure are not limited to just two set of perforations as described above. Any number of sets of perforations having progressively higher breakdown pressures may be broken down without diverting from the scope of the disclosure. For example, a complete wellbore may be perforated by a number of sets of perforations having progressively higher breakdown pressures by utilizing multiple diversion processes.

In one or more embodiments of the disclosure, a third perforation strategy may include generating a first group of production perforations along a wellbore having a first breakdown pressure and a second group of production perforations along a wellbore having a second breakdown pressure that is greater than the first breakdown pressure. The third perforation strategy may be used to fracture the geological formation surrounding the wellbore.

FIG. 10 shows a wellbore (1000) including low breakdown pressure perforations (1010) and high breakdown pressure perforations (1020) in accordance with one or more embodiments of the disclosure. As seen from FIG. 10, the perforations are arranged as a first group of low breakdown pressure perforations (1010) and high breakdown pressure perforations (1020). In one or more embodiments of the disclosure, the perforation depth and perforation direction of each of the perforations is selected to engineer the breakdown pressure of each perforation to correspond to a high breakdown pressure or a low breakdown pressure.

Once the perforations are formed, the geological formation surrounding the wellbore (1000) may be hydraulically fractured. Hydraulic fracturing may include pumping fluids into the wellbore until the low breakdown pressure perforations (1010) are broken down.

FIG. 11 shows the wellbore (1000) after breaking down the low breakdown pressure perforations (1010) in accordance with one or more embodiments of the disclosure. Breaking down the low breakdown pressure perforations (1010) may generate a first set of fractures (1100), extending into the geological formation surrounding the wellbore (1000), corresponding to the low breakdown pressure perforations (1010). Once the low breakdown pressure perforations (1010) are broken down, a seat (1110), previously installed in the wellbore (1000) may be sealed by pumping a single ball or other sealing component into the wellbore (1010). Sealing the seat (1110) may isolate the low breakdown pressure perforations (1010) from subsequent hydraulic fracturing operations.

After temporarily sealing the seat (1110), the pressure in the wellbore may be increased to breakdown the high breakdown pressure perforations (1020). By breaking down the high breakdown pressure perforations (1020) the fluid mobility within the geological formation may be improved. Thus, the third perforation strategy may improve the flow of fluid within a geological formation surrounding a wellbore (1000) by sequentially isolating broken down perforations by a seat (1110) and pumped down sealing component such as a ball.

While the three perforation strategies above have been described as having a single diversion process, a perforation strategy in accordance with one or more embodiments of the disclosure may include any number of diversion processes and associated groupings of perforations based on a breakdown pressure of each perforation. For example, perforations along a wellbore could be engineered to have approximately four levels of breakdown pressures, based on the measured or computed stresses along the wellbore as described above. Each group of perforation having an associated breakdown pressure could be broken down and temporarily sealed by a sequential process of increasing the pressure in the wellbore to the next lowest breakdown pressure of a group of perforations and then pumping diversion materials into the wellbore.

Returning to FIG. 1, at item 10200, a hydraulic fracturing plan may be determined based on the flow rate of each perforation. A hydraulic fracturing plan, sometime referred to as a hydraulic fracturing schedule, is a sequential lists of pumping operations. Each pumping operating includes a fluid type, pumping rate, and pumping duration. When a perforation along a wellbore breaks down in response to pressurized fluids within the wellbore exerting pressure on the perforation, fluids within the wellbore may begin to flow into the geological formation through the broken down perforation. To attain the pressures within the wellbore that will breakdown the perforations, the fluid flowing into the geological formation through the broken down perforations is considered.

In one or more embodiments of the disclosure, the flow rate of an operation of the hydraulic fracturing plan to breakdown a group of perforations may be determined by iteratively calculating which perforations are broken down for a given flow rate. The perforations are ordered, from lowest to highest, based on the breakdown pressure of each perforation. The perforation having the lowest breakdown pressure is assumed to be broken down. The flow rate through the perforation is calculated by:

q _(i)=sqrt((C _(d,i) ² ×d _(p,i) ²×(p _(wb) −p _(min stress,i)))/(0.237×ρ)  (Equation 1)

where

q_(i)=flow rate through perforation

C_(d,i)=Discharge coefficient

d_(p,i)=perforation diameter

p_(wb)=Wellbore pressure

p_(min stress,i)=minimum horizontal stress

ρ=fluid density

i=perforation number ordered from lowest to highest breakdown pressure

Using equation 1, p_(wb) is adjusted until q_(i)=the given flow rate. If p_(wb) is greater than the breakdown pressure of the next lowest breakdown pressure perforation, the next lowest breakdown pressure perforation is assumed to be opened and the calculation is repeated, adjusting p_(wb) until the given flow rate is equal to the sum of the flow rates of each of the broken down perforations. The above process is sequentially repeated for given flow rates until, for a given flow rate, the perforations that are to be broken down during a given operation of a hydraulic fracturing schedule are determined as broken down.

The above process may be used to determine the given flow rate for each fracturing process for a hydraulic fracturing schedule that includes diversion processes, e.g. processes that temporarily seal perforations. For example, a hydraulic fracturing schedule may include four pumping processes separated by three diversion processes. A flow rate for the first pumping process may be determined as described above without modification. For the second through fourth pumping processes, some of the perforations may be temporarily sealed. For each of the temporarily sealed perforations, the flow rate into the perforation is assumed to be zero rather than calculated by Equation 1. Thus, the flow rate for each pumping operation of a hydraulic fracturing plan may be determined based on the flow rate of each of the perforations. The hydraulic fracturing plan may be updated based on the determined flow rates for each pumping operation of the hydraulic fracturing plan.

While the method of determining a hydraulic fracture plan as described above may be used to determine a hydraulic fracturing plan for any of the three fracturing strategies described in 10100, the method of determining a hydraulic fracturing plan disclosed in item 10200 (FIG. 1) may be applied to any number of perforation strategies.

For example, before perforating a wellbore in item 10100 (FIG. 1), a fourth perforation strategy may be to equalize the rate of fluid flow into a set of perforations. Equalizing the rate of fluid flow into the set of perforations may improve the uniformity and conductivity of fractures generated during hydraulic fracturing. To equalize the fluid flows into the set of perforations, prototype sets of perforations may be rapidly evaluated by computationally or analytically determining the breakdown pressure for each perforation in a prototype set of perforations as described in item 10100 (FIG. 1). Based on the determined breakdown pressures, the flow rate into each perforation of the prototype set of perforations may be determined as described in item 10200 (FIG. 1). If the flow rate into each perforation of the prototype set of perforations is not approximately equal, the location, diameter, penetration direction, or depth may be modified to improve the uniformity of each flow rate. The updated set of perforations may be evaluated as describe above and the above process may be repeated until the uniformity of the flow rate of the perforations is approximately equal.

At item 10300, the geological formation is hydraulically fractured based on the hydraulic fracturing plan. As discussed above, the hydraulic fracturing plan is determined based on the computed flow rates of each perforation. Hydraulically fracturing the geological formation may generate fractures extending from the wellbore into the geological formation

At 10400, the hydraulically fractured well is evaluated by a Modified Step-Down Test (MSDT). The MSDT is a fluid flow-fluid pressure test that may be performed at the beginning of a hydraulic fracturing process. The MSDT may characterize aspects of fluid flow within the geological formation and the wellbore.

The MSDT may include pumping fluid into the wellbore at a first rate for a first period of time. The pumping rate may then be decreased to a second pumping rate and fluid may be pumped at the second pumping rate for a second period of time. The process is then repeated until the pumping rate reaches zero. During the MSDT, the bottom hole pressure is either measured directly or calculated by indirect measurements for the duration of the MSDT.

FIG. 12 shows a plots of the pumping rate (1200) and the bottom hole pressure (1210) during an example MSDT in accordance with one or more embodiments of the disclosure. In FIG. 12, the horizontal axis corresponds to the treatment time, the left vertical axis corresponds to the bottom hole pressure, and the right vertical axis corresponds to the fluid pumping rate. As seen from FIG. 12, the example MSDT included five stages. The pumping rate for each stage was approximately 60, 50, 38, 25, and 12 barrels per minute, respectively. Also, as seen from FIG. 12, the measured bottom hole pressure varies with time for each stage of the MSDT. Graphical arrows (1220) have been superimposed over the plot to indicate the change of the bottom hole pressure each stage of the MSDT.

After performing the MSDT, the rate of change of the bottom hole pressure during each stage of the MSDT is determined (as represented by the slope of the arrows (1220)). In one or more embodiments of the disclosure, the rate of change of the bottom hole pressure may be calculated by numerical differentiation or other numerical method as known in the art. The calculated rate of change of the bottom hole pressure for each stage may then be normalized the volume of fluid pumped during the stage, e.g., the rate of change of the bottom hole pressure for each stage may be divided by the volume of fluid pumped during the stage. The normalized rate of change of the bottom hole pressure for each stage may be plotted versus the flow rate of each stage.

FIG. 13A-13C show example plots of the normalized rate of change of the bottom hole pressure versus the pumping rate for each stage of a MSDT in accordance with one or more embodiments of the disclosure. Specifically, the horizontal axis of each plot corresponds to the fluid pumping rate and the vertical axis corresponds to the rate of change of the bottom hole pressure divided by the injection volume.

In FIG. 13A, the magnitude of the normalized rate of change of the bottom hole pressure increases as the injection rate increases. This result is the expected result for a hydraulically fractured well in a permeable geologic formation where some of the fluid being injected is leaking off into the rock matrix with the remaining fluid being used to create the fracture dimensions. By interpolating a line through the measured point, one can estimate where that line passes through the 0 point (dP/dV=0). This point represents the rate at which fluid being injected into the fracture is equal to the rate that fluid is flowing out of the fracture (into the matrix), and thus can be used as a representation of fluid leak-off rates which is used in fracture modeling.

In FIG. 13B, the magnitude of the normalized rate of change of the bottom hole pressure is constant, regardless of injection rate. A constant magnitude may indicate that there is negligable leak off into formation which would be expected in most shale reservoirs with extremely low permeability. A constant positive value may indicate that the fracture is growing in length, and have very good height containment. If the value is at or near 0, one would expect a fracture that is growing radially where fracture height and length are increasing, while a constant negative value may indicate that the fracture is closing such as when there is fracture height growth.

In FIG. 13C, the magnitude of the normalized rate of change of the bottom hole pressure increases as the injection rate decreases. A decreasing normalized rate of change of the bottom hole pressure may indicate tortuosity along the wellbore may exist. This tortuosity may inhibit fracturing fluids from entering the formation, and may additionally cause a reduced width in the near wellbore area that could potentially inhibit proppant from entering the fracture. To remedy a perceived high tortuosity condition, common practice may include pumping a more viscous fluid, pumping at a high rate or re-perforating the interval.

While the MSDT is described above as being performed at the beginning of a hydraulic fracturing operation, the MSDT may be performed at any time without departing from the scope of the disclosure. Performing the MSDT at the end of a hydraulic fracturing operation, for example, may be used to calibrate the fluid friction within completion components of the well.

Returning to FIG. 1, at item 10500, hydrocarbon bearing fluids may be produced based on the evaluation of the wellbore by the MSDT. As described above, the MSDT may indicate that additional processes need to be performed on the wellbore or the fractures in the geological formation surrounding the wellbore. Once the processes indicated by the MSDT in item 10400 are complete, hydrocarbon bearing fluids may be produced from the well by any method known in the art.

Thus, the method disclosed in FIG. 1 may improve the production of hydrocarbon baring fluids from a wellbore, reduce complications in placing the hydraulic fractures by, for example, reducing treatment pressures, decrease the quantity of fluids or materials used to fracture a geological formation, and/or decrease the number of stages of a hydraulic fracturing process when compared to a traditional hydraulic fracturing process.

Embodiments of the disclosure may be implemented on virtually any type of computing system, regardless of the platform being used. For example, the computing system may be one or more mobile devices (e.g., laptop computer, smart phone, personal digital assistant, tablet computer, or other mobile device), desktop computers, servers, blades in a server chassis, or any other type of computing device or devices that includes at least the minimum processing power, memory, and input and output device(s) to perform one or more embodiments. For example, as shown in FIG. 14, the computing system (1400) may include one or more computer processor(s) (1402), associated memory (1404) (e.g., random access memory (RAM), cache memory, flash memory, etc.), one or more storage device(s) (1406) (e.g., a hard disk, an optical drive such as a compact disk (CD) drive or digital versatile disk (DVD) drive, a flash memory stick, etc.), and numerous other elements and functionalities. The computer processor(s) (1402) may be an integrated circuit for processing instructions. For example, the computer processor(s) may be one or more cores, or micro-cores of a processor. The computing system (1400) may also include one or more input device(s) (1410), such as a touchscreen, keyboard, mouse, microphone, touchpad, electronic pen, or any other type of input device. Further, the computing system (1400) may include one or more output device(s) (1408), such as a screen (e.g., a liquid crystal display (LCD), a plasma display, touchscreen, cathode ray tube (CRT) monitor, projector, or other display device), a printer, external storage, or any other output device. One or more of the output device(s) may be the same or different from the input device(s). The computing system (1400) may be connected to a network (1412) (e.g., a local area network (LAN), a wide area network (WAN) such as the Internet, mobile network, or any other type of network) via a network interface connection (not shown). The input and output device(s) may be locally or remotely (e.g., via the network (1412)) connected to the computer processor(s) (1402), memory (1404), and storage device(s) (1406). Many different types of computing systems exist, and the aforementioned input and output device(s) may take other forms.

Software instructions in the form of computer readable program code to perform embodiments may be stored, in whole or in part, permanently, on a non-transitory computer readable medium such as a CD, DVD, storage device, a diskette, a tape, flash memory, physical memory, or any other non-transitory computer readable storage medium. Specifically, the software instructions may correspond to computer readable program code that when executed by a processor(s), is configured to perform embodiments.

Further, one or more elements of the aforementioned computing system (1400) may be located at a remote location and connected to the other elements over a network (1412). Further, one or more embodiments may be implemented on a distributed system having a plurality of nodes, where each portion such as the first program, second program, and the third program may be located on a different node within the distributed system. In one embodiment, the node corresponds to a distinct computing device. In another embodiment, the node may correspond to a computer processor with associated physical memory. The node may correspond to a computer processor or micro-core of a computer processor with shared memory and/or resources.

While the disclosure has been described above with respect to a limited number of embodiments, those skilled in the art, having the benefit of this disclosure, will appreciate that other embodiments can be devised which do not depart from the scope of the disclosure as disclosed herein. Accordingly, the scope of the disclosure should be limited by the attached claims. 

What is claimed is:
 1. A method, comprising: determining a stress variation of a geological formation disposed on a wellbore; determining a breakdown pressure of each perforation of a plurality of perforations along a length of the wellbore based on the stress variation; calculating a flow rate of a pumping operation of a hydraulic fracturing process based on the breakdown pressure of each perforation of the plurality of perforations; hydraulically fracturing a geological formation disposed on the wellbore based on the flow rate.
 2. The method according to claim 1, wherein the stress variation is along a length of the wellbore.
 3. The method according to claim 1, wherein the stress variation is about a cross section of the wellbore.
 4. The method according to claim 1, wherein calculating the flow rate comprises: ordering each perforation of the plurality of perforations based on the breakdown pressure of each perforation; determining the flow rate through the perforation having a lowest breakdown pressure for a test flow rate into the wellbore; determining a breakdown state of a perforation of the plurality of perforations having a breakdown pressure greater than the lowest breakdown pressure based on the test flow rate.
 5. A method, comprising: determining a stress variation of a geological formation disposed on a wellbore; generating a first plurality of perforations having a having a first breakdown pressure and a second plurality of perforations having a second breakdown pressure greater than the first breakdown pressure based on the stress variation; hydraulically fracturing a first portion of the geological formation corresponding to the first plurality of perforations; isolating the first plurality of perforations; hydraulically fracturing a second portion of the geological formation corresponding to the second plurality of perforations.
 6. The method according to claim 5, wherein each perforation of the first plurality of perforations has a location along the wellbore corresponding to a low stress location of the stress variation.
 7. The method according to claim 5, wherein each perforation of the second plurality of perforations has a location along the wellbore corresponding to a high stress location of the stress variation.
 8. The method according to claim 5, wherein each perforation of the first plurality of perforations has a perforation direction corresponding to a low stress perforation direction of the stress variation.
 9. The method according to claim 5, wherein each perforation of the second plurality of perforations has a perforation direction corresponding to a high stress perforation direction of the stress variation.
 10. The method according to claim 5, further comprising: overflushing the wellbore while the first plurality of perforations is isolated; removing the isolation of the first plurality of perforations.
 11. A method, comprising: determining a stress variation of a geological formation disposed on a wellbore; generating a first plurality of perforation groups having a first breakdown pressure based on the stress variation; generating a second plurality of perforation groups having a second breakdown pressure based on the stress variation; hydraulically fracturing a first portion of the geological formation corresponding to the first plurality of perforation groups; isolating the first plurality of perforation groups; hydraulically fracturing a second portion of the geological formation corresponding to the second plurality of perforation groups.
 12. The method according to claim 11, wherein the majority of each perforation group of the first plurality of perforation groups is disposed along the wellbore at a location where a nearest neighboring perforation group is a perforation group of the second plurality of perforation groups.
 13. The method according to claim 11, wherein each perforation group of the first plurality of perforation groups is disposed along a first length of the wellbore and each perforation group of the second plurality of perforation groups is located along a second length of the wellbore.
 14. The method according to claim 11, wherein each perforation group of the first plurality of the first plurality of perforation groups has a perforation depth based on the first breakdown pressure.
 15. The method according to claim 11, wherein each perforation group of the first plurality of the first plurality of perforation groups has a perforation direction based on the first breakdown pressure.
 16. A method, comprising: pumping a fluid into a wellbore at a first rate for a first period of time and determining a first bottom hole pressure; determining a rate of change of the first bottom hole pressure during the first time period; normalizing the determined rate of change of the bottom hole pressure to a volume of the fluid pumped during the first time period.
 17. The method according to claim 16, further comprising: pumping the fluid into the wellbore at a second rate for a second period of time and determining a second bottom hole pressure; determining a second rate of change of the second bottom hole pressure during the second time period; normalizing the determined second rate of change of the second bottom hole pressure to a second volume of the fluid pumped during the second time period, wherein the second rate is less than the first rate.
 18. The method according to claim 17, further comprising: determining a state of the wellbore based on the normalized first rate of change of the first bottom hole pressure and the normalized second rate of change of the second bottom hole pressure.
 19. The method according to claim 18, wherein the state of the wellbore is determined as highly tortuous if the magnitude of the normalized first rate of change of the first bottom hole pressure is less than magnitude of the normalized second rate of change of the second bottom hole pressure.
 20. The method according to claim 18, further comprising: determining a leakoff rate by interpolating a rate at which a normalized rate of pressure change is reduced to zero based on the normalized first rate of change of the first bottom hole pressure and normalized second rate of change of the second bottom hole pressure. 